In recent years the femtoscopy technique has been used by the ALICE Collaboration in small colliding systems at the LHC to investigate the strong-interaction of hadron pairs in the low-energy regime. The extension of this technique to the study of many-body correlations aims to deliver in the next years the first experimental measurements of the genuine many-hadron interactions, provided that the contributions due to the lower order terms are properly accounted for. In this paper we present a method that allows to determine the residual lower order contributions to the three-body correlation functions, based on the cumulant decomposition approach and on kinematic transformations. A procedure to simulate genuine three-body correlations in three-baryon correlation functions is also developed. A qualitative study of the produced correlation signal is performed by varying the strength of the adopted three-body interaction model and comparisons with the expectations for the lower order contributions to the correlation function are shown. The method can be also applied to evaluate the combinatorial background in the two-body correlation functions, providing an improved statistical accuracy with respect to the standard techniques. The example of the contribution by the pK + K - channel to the recently measured p ϕ correlation is discussed.